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Entropy
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Dispersion Entropy: Theory and Applications
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Dispersion Entropy: Theory and Applications

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Multidisciplinary Applications".

Deadline for manuscript submissions: closed (15 April 2023) | Viewed by 7842

Special Issue Editors

Dr. Anne Humeau-Heurtier

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Guest Editor
Laboratoire Angevin de Recherche en Ingénierie des Systèmes (LARIS), University of Angers, IUT, GEII Department, 4 boulevard Lavoisier, BP 42018, CEDEX, 49016 Angers, France
Interests: entropy; multiscale entropy; nonlinear analysis; empirical mode decomposition; biomedical data
Special Issues, Collections and Topics in MDPI journals
Dr. Hamed Azami

E-Mail Website
Guest Editor
Research Fellow in Biomedical Signal Processing & Machine Learning, University of Toronto, Toronto, ON M5S 1A1, Canada
Interests: biomedical signal processing; nonlinear analysis; brain–computer interface; machine learning
Special Issues, Collections and Topics in MDPI journals
Dr. Mostafa Rostaghi

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Guest Editor
Department of Mechanical Engineering, Semnan University, Semnan 35131-19111, Iran
Interests: signal processing; fault diagnosis; vibration
Dr. Daniel Abasolo

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Guest Editor
Centre for Biomedical Engineering, Department of Mechanical Engineering Sciences, Faculty of Engineering and Physical Sciences, University of Surrey, Guildford GU2 7XH, UK
Interests: biomedical signal processing; entropy; complexity; machine learning; electroencephalogram; magnetoencephalogram; Alzheimer’s disease; healthy ageing; epilepsy
Special Issues, Collections and Topics in MDPI journals
Dr. Javier Escudero

E-Mail Website
Guest Editor
School of Engineering, Institute for Digital Communications, University of Edinburgh, Edinburgh EH9 3FB, UK
Interests: connectivity; biomedical signal processing; nonlinear analysis; brain activity; multiway array analysis
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

In this Special Issue, we would like to collect papers focusing on both the theory and applications of dispersion entropy and its modified forms (fluctuation and fuzzy dispersion entropy). Despite being a very recent technique, dispersion entropy has received substantial and still increasing attention in the field, having found interesting applications in a wide range of fields, including the analysis of biomedical signals, mechanical systems, marine science, the economy, civil engineering, and computer science, among others. Moreover, dispersion entropy has spurred new theoretical developments, including variations of dispersion entropy for univariate time series and versions of the algorithm for multivariate time series, 2D images, 3D data, and multiscale implementations.

However, opportunities, both in theoretical advances and practical applications, are abundant. As such, this Special Issue seeks to serve as a vehicle for the exploration of these emerging topics. As a result, the main topics of this Special Issue include (but are not limited to):

  • Reviews on diverse aspects of dispersion entropy.
  • Theoretical developments enabled by the concepts of dispersion entropy and dispersion patterns.
  • Studies comparing dispersion entropy with other nonlinear analysis techniques.
  • Studies of the behavior of dispersion entropy in relation to other signal characteristics.
  • Explorations of the relationships between dispersion entropy and other descriptions of complex and nonlinear systems, including network analysis and connectivity.
  • Investigation of underlying mechanisms behind dispersion entropy results used for physiological data to improve our understanding of disease diagnosis/pathogenesis/progression.
  • Theoretical and practical considerations of the parameters used in dispersion entropy, including the mapping function, embedding dimension, time delay, and sampling frequency, in the characterization of data with different lengths and signal-to-noise ratios.
  • Applications of dispersion entropy including, but not limited to, biomedical, mechanical, financial, and climatological data.

Dr. Anne Humeau-Heurtier
Dr. Hamed Azami
Dr. Mostafa Rostaghi
Dr. Daniel Abasolo
Dr. Javier Escudero
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Published Papers (5 papers)

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Research

26 pages, 4396 KiB  
Article
Refined Composite Multiscale Fuzzy Dispersion Entropy and Its Applications to Bearing Fault Diagnosis
by Mostafa Rostaghi, Mohammad Mahdi Khatibi, Mohammad Reza Ashory and Hamed Azami
Entropy 2023, 25(11), 1494; https://doi.org/10.3390/e25111494 - 29 Oct 2023
Cited by 1 | Viewed by 1033
Abstract
Rotary machines often exhibit nonlinear behavior due to factors such as nonlinear stiffness, damping, friction, coupling effects, and defects. Consequently, their vibration signals display nonlinear characteristics. Entropy techniques prove to be effective in detecting these nonlinear dynamic characteristics. Recently, an approach called fuzzy [...] Read more.
Rotary machines often exhibit nonlinear behavior due to factors such as nonlinear stiffness, damping, friction, coupling effects, and defects. Consequently, their vibration signals display nonlinear characteristics. Entropy techniques prove to be effective in detecting these nonlinear dynamic characteristics. Recently, an approach called fuzzy dispersion entropy (DE–FDE) was introduced to quantify the uncertainty of time series. FDE, rooted in dispersion patterns and fuzzy set theory, addresses the sensitivity of DE to its parameters. However, FDE does not adequately account for the presence of multiple time scales inherent in signals. To address this limitation, the concept of multiscale fuzzy dispersion entropy (MFDE) was developed to capture the dynamical variability of time series across various scales of complexity. Compared to multiscale DE (MDE), MFDE exhibits reduced sensitivity to noise and higher stability. In order to enhance the stability of MFDE, we propose a refined composite MFDE (RCMFDE). In comparison with MFDE, MDE, and RCMDE, RCMFDE’s performance is assessed using synthetic signals and three real bearing datasets. The results consistently demonstrate the superiority of RCMFDE in detecting various patterns within synthetic and real bearing fault data. Importantly, classifiers built upon RCMFDE achieve notably high accuracy values for bearing fault diagnosis applications, outperforming classifiers based on refined composite multiscale dispersion and sample entropy methods. Full article
(This article belongs to the Special Issue Dispersion Entropy: Theory and Applications)
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15 pages, 3564 KiB  
Article
Variable-Step Multiscale Fuzzy Dispersion Entropy: A Novel Metric for Signal Analysis
by Yuxing Li, Junxian Wu, Shuai Zhang, Bingzhao Tang and Yilan Lou
Entropy 2023, 25(7), 997; https://doi.org/10.3390/e25070997 - 29 Jun 2023
Cited by 1 | Viewed by 974
Abstract
Fuzzy dispersion entropy (FuzDE) is a newly proposed entropy metric, which combines the superior characteristics of fuzzy entropy (FE) and dispersion entropy (DE) in signal analysis. However, FuzDE only reflects the feature from the original signal, which ignores the hidden information on the [...] Read more.
Fuzzy dispersion entropy (FuzDE) is a newly proposed entropy metric, which combines the superior characteristics of fuzzy entropy (FE) and dispersion entropy (DE) in signal analysis. However, FuzDE only reflects the feature from the original signal, which ignores the hidden information on the time scale. To address this problem, we introduce variable-step multiscale processing in FuzDE and propose variable-step multiscale FuzDE (VSMFuzDE), which realizes the characterization of abundant scale information, and is not limited by the signal length like the traditional multiscale processing. The experimental results for both simulated signals show that VSMFuzDE is more robust, more sensitive to dynamic changes in the chirp signal, and has more separability for noise signals; in addition, the proposed VSMFuzDE displays the best classification performance in both real-world signal experiments compared to the other four entropy metrics, the highest recognition rates of the five gear signals and four ship-radiated noises reached 99.2% and 100%, respectively, which achieves the accurate identification of two different categories of signals. Full article
(This article belongs to the Special Issue Dispersion Entropy: Theory and Applications)
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26 pages, 10443 KiB  
Article
A Fault Feature Extraction Method Based on Improved VMD Multi-Scale Dispersion Entropy and TVD-CYCBD
by Jingzong Yang, Chengjiang Zhou, Xuefeng Li, Anning Pan and Tianqing Yang
Entropy 2023, 25(2), 277; https://doi.org/10.3390/e25020277 - 02 Feb 2023
Cited by 4 | Viewed by 1351
Abstract
In modern industry, due to the poor working environment and the complex working conditions of mechanical equipment, the characteristics of the impact signals caused by faults are often submerged in strong background signals and noises. Therefore, it is difficult to effectivelyextract the fault [...] Read more.
In modern industry, due to the poor working environment and the complex working conditions of mechanical equipment, the characteristics of the impact signals caused by faults are often submerged in strong background signals and noises. Therefore, it is difficult to effectivelyextract the fault features. In this paper, a fault feature extraction method based on improved VMD multi-scale dispersion entropy and TVD-CYCBD is proposed. First, the marine predator algorithm (MPA) is used to optimize the modal components and penalty factors in VMD. Second, the optimized VMD is used to model and decompose the fault signal, and then the optimal signal components are filtered according to the combined weight index criteria. Third, TVD is used to denoise the optimal signal components. Finally, CYCBD filters the de-noised signal and then envelope demodulation analysis is carried out. Through the simulation signal experiment and the actual fault signal experiment, the results verified that multiple frequency doubling peaks can be seen from the envelope spectrum, and there is little interference near the peak, which shows the good performance of the method. Full article
(This article belongs to the Special Issue Dispersion Entropy: Theory and Applications)
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12 pages, 3482 KiB  
Article
Research on Twin Extreme Learning Fault Diagnosis Method Based on Multi-Scale Weighted Permutation Entropy
by Xuyi Yuan, Yugang Fan, Chengjiang Zhou, Xiaodong Wang and Guanghui Zhang
Entropy 2022, 24(9), 1181; https://doi.org/10.3390/e24091181 - 24 Aug 2022
Cited by 3 | Viewed by 1282
Abstract
Due to the complicated engineering operation of the check valve in a high−pressure diaphragm pump, its vibration signal tends to show non−stationary and non−linear characteristics. These leads to difficulty extracting fault features and, hence, a low accuracy for fault diagnosis. It is difficult [...] Read more.
Due to the complicated engineering operation of the check valve in a high−pressure diaphragm pump, its vibration signal tends to show non−stationary and non−linear characteristics. These leads to difficulty extracting fault features and, hence, a low accuracy for fault diagnosis. It is difficult to extract fault features accurately and reliably using the traditional MPE method, and the ELM model has a low accuracy rate in fault classification. Multi−scale weighted permutation entropy (MWPE) is based on extracting multi−scale fault features and arrangement pattern features, and due to the combination of extracting a sequence of amplitude features, fault features are significantly enhanced, which overcomes the deficiency of the single−scale permutation entropy characterizing the complexity of vibration signals. It establishes the check valve fault diagnosis model from the twin extreme learning machine (TELM). The TELM fault diagnosis model established, based on MWPE, aims to find a pair of non−parallel classification hyperplanes in the equipment state space to improve the model’s applicability. Experiments show that the proposed method effectively extracts the characteristics of the vibration signal, and the fault diagnosis model effectively identifies the fault state of the check valve with an accuracy rate of 97.222%. Full article
(This article belongs to the Special Issue Dispersion Entropy: Theory and Applications)
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16 pages, 25659 KiB  
Article
An Improved Incipient Fault Diagnosis Method of Bearing Damage Based on Hierarchical Multi-Scale Reverse Dispersion Entropy
by Jiaqi Xing and Jinxue Xu
Entropy 2022, 24(6), 770; https://doi.org/10.3390/e24060770 - 30 May 2022
Cited by 6 | Viewed by 1403
Abstract
The amplitudes of incipient fault signals are similar to health state signals, which increases the difficulty of incipient fault diagnosis. Multi-scale reverse dispersion entropy (MRDE) only considers difference information with low frequency range, which omits relatively obvious fault features with a higher frequency [...] Read more.
The amplitudes of incipient fault signals are similar to health state signals, which increases the difficulty of incipient fault diagnosis. Multi-scale reverse dispersion entropy (MRDE) only considers difference information with low frequency range, which omits relatively obvious fault features with a higher frequency band. It decreases recognition accuracy. To defeat the shortcoming with MRDE and extract the obvious fault features of incipient faults simultaneously, an improved entropy named hierarchical multi-scale reverse dispersion entropy (HMRDE) is proposed to treat incipient fault data. Firstly, the signal is decomposed hierarchically by using the filter smoothing operator and average backward difference operator to obtain hierarchical nodes. The smoothing operator calculates the mean sample value and the average backward difference operator calculates the average deviation of sample values. The more layers, the higher the utilization rate of filter smoothing operator and average backward difference operator. Hierarchical nodes are obtained by these operators, and they can reflect the difference features in different frequency domains. Then, this difference feature is reflected with MRDE values of some hierarchical nodes more obviously. Finally, a variety of classifiers are selected to test the separability of incipient fault signals treated with HMRDE. Furthermore, the recognition accuracy of these classifiers illustrates that HMRDE can effectively deal with the problem that incipient fault signals cannot be easily recognized due to a similar amplitude dynamic. Full article
(This article belongs to the Special Issue Dispersion Entropy: Theory and Applications)
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